This invention solves a basic problem in the metrology for high spatial resolution measurement of large structures with aspect ratios (or their equivalent) much larger than one. Typical applications might be the measurements of stick mirrors or the measurement of circular flatness of rings where the ring width is small compared to the ring diameter.
In the field of optics manufacturing, it has long been a problem to make accurate, high-resolution measurements of large flats. Similar problems arise for large convex spherical or aspheric optics, or spherical optics covering a very large included angle (for example hemispheres). Another common problem is measurement of optics with large slopes, for example aspheric optics used in astronomy, lithography etc.
One solution to this problem is sub-aperture stitching. FIG. 1 from United States Patent Publication No. 2003-0117632 published on Jun. 26, 2003 in the name of Golini, Donald, Forbes, Greg and Murphy, Paul; and entitled Method for self-calibrated sub-aperture stitching for surface figure measurement shows measurement of a large aperture optic (14) by measuring a number of overlapping sub-apertures (12) arranged in an appropriate pattern. Either the part or the interferometer is moved between measurements. This movement introduces errors so the data in the overlapping regions are matched mathematically to establish the relationship between the sub-apertures. As discussed in Assoufid (Lahsen Assoufid, Michael Bray, Jun Qian, Deming Shu, 3D surface profile measurements of large x-ray synchrotron radiation mirrors using stitching interferometry Proc. SPIE Vol. 4782, 2002, p. 21–28) and the references therein and Golini, et al. above, such procedures are subject to all the common errors of interferometry, plus some errors specific to stitching. Large-scale fluctuations result from the propagation of small errors in the individual measurements, which cause imperfections in the overlap region. Assoufid, et al. above point out that the propagation of errors that vary between sub-aperture measurements is reduced when there is a two-dimensional array of overlapping sub-apertures (as in FIG. 1). For the specific case of measuring a synchrotron mirror, they show the propagation of errors when a single line of sub-apertures were measured; in their case these errors were reduced by “double overlap”.
In view of the prior art, it is a primary object of the present invention to provide a mathematically stable procedure and apparatus for interferometrically measuring parts having large aspect ratios.
It is yet another object of this invention to provide procedures and apparatus by which the surfaces of high aspect ratio parts may more precisely be measured using low resolution and high resolution measurements which in their mathematical treatment compensate for systematic errors in part staging while permitting combination of sub aperture interferometric measurements without the use of overlap.
Other objects of the invention will be obvious, in part, and others will appear, in part, in the following detailed description when read in connection with the accompanying drawings.